1991 AMC 12 Problem 16

Question

One hundred students at Century High School participated in the AHSME last year, and their mean score was

100.

The number of non-seniors taking the AHSME was

50\%

more than the number of seniors, and the mean score of the seniors was

50\%

higher than that of the non-seniors. What was the mean score of the seniors?

100

112.5

120

125

150

First determine the numbers of seniors and non-seniors

Let the non-senior mean be

x

and form a weighted-average equation

If there are

s

seniors, then there are

1.5s

non-seniors, so

2.5s=100

and

s=40.

Let the non-senior mean be

x;

the senior mean is

1.5x.

The total score equation is

60x+40(1.5x)=100(100),

so

120x=10000,

and the senior mean is

1.5x=125.

Thus the correct answer is D.

Problem 16 in other years